Theory of Numbers (V63.0248) Professor M. Hausner
The text for this course is:
An Introduction to the Theory of Numbers, Fifth Edition by Niven, Zuckerman & Montgomery
John Wiley & Sons, Inc.
The course meets Mondays through Thursday, from May 14 through June 22. Time 1:00
PM to 3:05 PM. (Note change in time.)
The course will cover topics from the following list:
1. Divisibility: Division algorithm; the Euclidian algorithm
2. Prime numbers: the infinitude of prime; the unique factorization theorem.
3. The Sieve of Eratosthenes.
4. The binomial theorem; binomial coefficients.
5. Congruences. The Chinese Remainder Theorem
6. Euler’s φ function.
7. Fermat’s little theorem, and Euler’s generalization.
8. Application to cryptography.
9. Groups and fields in number theory.
10. Primitive roots.
11. Quadratic congruences.
12. Quadratic reciprocity.
Homework based on the lectures and text will be posted on Tuesdays (due the following
Thursday) and Friday (due the Monday following). Late homework will not be accepted.
There will be a mid-term exam on Monday, June 4th. The final exam will be given on the last day of class. The final grade is based on the homework (30%), mid-term (30%) and final exam (40%).
Some basic contact information:
I am located on the 7th floor of Warren Weaver Hall.
Room number is 706.
Phone is 212-998-3162 direct.
E-mail: hausner@cims.nyu.edu. (The best way to contact me.)
Office hours: Mondays and Wednesdays, my office, from 11 to 12. And by appointment.
If you are having trouble with the course, or want to talk to me about the material, please don’t hesitate to call or write.